elliptic geometry

Học thuật
Thân thiện
elliptic geometry

A student draws a diagram of elliptic geometry on a chalkboard.

Definition
  1. Noun:
    • A branch of non-Euclidean geometry in which space is modeled as having properties analogous to the surface of a sphere. In this geometry, there are no parallel lines, and the sum of the angles in a triangle is always greater than 180 degrees.
Usage
  • Elliptic geometry provides a mathematical framework for describing curved spaces, such as the surface of a sphere.
  • The study of elliptic geometry is fundamental to understanding the geometry of the universe in certain cosmological models.
  • In elliptic geometry, the concept of a "straight line" is replaced by the concept of a geodesic, like a great circle on a sphere.
Examples
  • The mathematician explored the properties of triangles in elliptic geometry.
  • Elliptic geometry challenges the Euclidean postulate that through a point not on a given line, exactly one line can be drawn parallel to the given line.
  • Understanding elliptic geometry is essential for certain applications in astronomy and general relativity.
Advanced Usage
  • Riemannian geometry is a broad generalization that includes elliptic geometry as a special case.
  • The geometry of a sphere is a simple, intuitive model for understanding the principles of elliptic geometry.
Variants and Related Words
  • Elliptical (adjective): Pertaining to or having the form of an ellipse. (Note: While related, "elliptical" in common usage often refers to the shape of an oval, whereas "elliptic" in this context refers to a specific type of geometry).
  • Riemannian geometry (noun): A more general form of non-Euclidean geometry developed by Bernhard Riemann, which includes elliptic geometry.
  • Spherical geometry (noun): Often used synonymously with elliptic geometry, especially in its two-dimensional form on the surface of a sphere.
Synonyms
  • Riemannian geometry (in a specific sense)
  • Spherical geometry
Related Concepts (Not Phrasal Verbs or Idioms)
  • Non-Euclidean geometry: The overarching category of geometries that do not obey all of Euclid's postulates, which includes elliptic geometry.
  • Great circle: The analogue of a "straight line" in the spherical model of elliptic geometry; it is the intersection of a sphere with a plane passing through its center.
  • Gaussian curvature: A measure of the intrinsic curvature of a surface; elliptic geometry is characterized by constant positive curvature.
elliptic geometry

A student draws a diagram of elliptic geometry on a chalkboard.

Noun
  1. (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle
    • Bernhard Riemann pioneered elliptic geometry

Từ đồng nghĩa